De-modulation of MOK (M-ary orthogonal modulation)

ABSTRACT

A system and method for the iterative detection and demodulation of M-ary orthogonal signals (MOK) and signals modulated using Complementary Code Keying (CCK) is described. An important feature of these methods is the good performance of noncoherent detectors in AWGN channels. However, the performance of these detectors in fast fading channels degrades considerably compared to that of coherent detectors. Iterative detection algorithms that significantly improve the performance of the demodulators with minimal additional complexity are presented The methods use soft decoder output feedback and iterative demodulation and decoding to achieve performance close to that of coherent detection. For MOK, significant performance enhancement is possible even without any loss of throughput due to insertion of pilot symbols. For CCK pilot symbols are necessary but the throughput loss remains low.

FIELD OF THE INVENTION

The present invention relates to the detection and demodulation of M-aryorthogonal signals (MOK) and Complementary Code Keying (CCK) signals, inparticular by using an iterative combination of noncoherent and coherentsystems and methods.

BACKGROUND OF THE INVENTION

There is a move towards high data rate transmission in wirelesscommunication systems. Efforts are now directed towards developingwireless systems that provide data rates on the order of 10 Mb/s. Toachieve these high rates there has been a search for modulation schemesmore efficient than M-ary PSK.

Different forms of orthogonal modulation have been considered andadopted by various standards committees. A form of orthogonal modulationwas adopted in the IS-95 standard as the modulation technique used forthe return link. J=log₂ M bits are transmitted per symbol and one of Morthogonal binary sequences known as the Hadamard-Walsh functions isselected for transmission. This technique is called M-ary orthogonalkeying (MOK).

One of the main advantages of MOK is the ability to demodulate thesignals noncoherently with minimal performance degradation. Compared todifferential PSK, noncoherent detection of MOK has a much betterperformance and so it has been considered by a number of differentstandards. MOK may have better BER performance than BPSK, which is dueto the embedded coding properties of MOK For the above mentionedadvantages, MOK is considered a great choice for reverse linkcommunications, where there is usually no pilot or reference signal toassist coherent detection.

For Additive White Gaussian Noise (AWGN) channel, the performancedifference between noncoherent and coherent detection of MOK is lessthan 1 dB for M>2. For fast fading channels, the performance ofnoncoherent detection may be several dBs worse than that of coherentdetection. Practical systems, especially terrestrial mobilecommunication systems with low SNR and severe fading, concatenate MOKwith a form of forward error correction, usually convolutional codes.The present invention could work for MOK with any kind of outer coding.That is, the outer code need not be a convolutional code, but any codethat can be decoded while generating soft decoder outputs. Optimumreception of this scheme is to implement one maximum likelihoodreceiver, which is very complex to implement. For near optimum receptionof this coded system, soft detection information should be exchangedbetween the different blocks of the receiver.

SUMMARY OF THE INVENTION

A method where convolutionally coded data is orthogonally modulatedusing MOK is presented. At the receiver, following the noncoherentdetection of the MOK symbols, a simple metric is calculated and passedto the MAP decoder to decode the symbols. Following decoding, the softdecoder outputs are then used to calculate the probabilities ofdifferent symbols, a channel estimator is used to estimate the fadingchannel and help re-demodulate the MOK signal coherently. The steps ofdecoding and channel estimation are then iteratively repeated untilthere is no gain or recognition improvement or until the recognitionimprovement is outweighed by the effort to achieve the recognitionimprovement.

That is, a method is presented for use in a receiver for detecting anddemodulating M-ary orthogonal signals (MOK) comprising the steps ofreceiving convolutionally coded M-ary orthogonally modulated symbolsover a channel, demodulating said M-ary orthogonally modulated symbols,calculating a metric, decoding said symbols, calculating probabilitiesof different symbols for each symbol instance, estimating a fadingchannel responsive to calculating the probabilities and iterativelyfeeding said metric, said decoded symbols, said probabilities and saidestimate back into said demodulating step to re-demodulate said symbolscoherently. The method may also include interleaving on the transmitterside and corresponding de-interleaving on the receiving side.

The method has been tested for Rayleigh and Rician fading channels withdifferent fading rates where it shows considerable improvement overconventional noncoherent detection especially for fast fading channels.

An improvement to the first embodiment using a quasi-coherent detectoris presented. It was noticed that all the MOK symbols start with a “1”so a form of symbol aided demodulation (SAD) is applied to the MOKsignals. A method that uses the known first chip of every symbol ispresented and tested for fading channels. A comparison between the twomethods is presented graphically.

A similar technique called complementary code keying (CCK) has beenadopted by the IEEE 802.11 subcommittee for wireless local are networks(WLAN) for transmission of data rates of 5.5 and 11 Mb/s. CCK is ageneralized form of (M-ary biorthogonal keying) MBOK.

After studying the application of CCK for terrestrial fast fadingcommunication channels, it was found that for fast fading channels, theperformance of noncoherent detection of CCK is significantly worse thanthat of the coherent detectors, even more than that encountered in theMOK case. A second alternative embodiment of the present invention is amodification for the existing CCK systems that greatly enhances theperformance of CCK for fast fading channels. The second embodimentpresents a method for use in a receiver for detecting and demodulating asignal of complementary code keying (CCK) symbols comprising the stepsof receiving complementary coded keying (CCK) modulated symbols over achannel, demodulating said complementary code keying modulated symbols,decoding said symbols, adding an extra known chip at a beginning ofevery symbol, calculating probabilities of different symbols for eachsymbol instance, calculating expected values of complex conjugates ofevery chip, estimating the fading channel at different chip positionswithin said symbol and iteratively feeding said decoded symbols, saidprobabilities and said estimate back into said demodulating step tore-demodulate said symbols.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described in greater detail withreference to the preferred embodiments of the invention, given only byway of example, and illustrated in the accompanying drawings in which:

FIG. 1 shows the block diagram of the noncoherent-coherent system.

FIG. 2 shows the method to construct the signal set for MOK.

FIG. 3 depicts a bank of M orthogonal noncoherent correlators, which isthe optimum detector for Hadamard-Walsh orthogonal modulation.

FIG. 4 shows the optimum coherent receiver.

FIG. 5 shows the performance of coherent and noncoherent detection oforthogonally modulated convolutionally coded signals in AWGNenvironment.

FIG. 6 shows the performance for MOK, for M=8 in Rayleigh fading channelwith a fading rate of 10.

FIG. 7 shows the performance for MOK, for M=8 in Rician fading channelwith a fading rate of 10.

FIG. 8 shows the performance for MOK, for M=8 in Rayleigh fading channelwith a fading rate of 40.

FIG. 9 shows the performance for MOK, for M=8 in Rician fading channelwith a fading rate of 40.

FIG. 10 shows the performance for MOK, for M=16 in Rayleigh fadingchannel with a fading rate of 20.

FIG. 11 shows the performance for MOK, for M=16 in Rician fading channelwith a fading rate of 20.

FIG. 12 shows the performance for MOK, for M=16 in Rayleigh fadingchannel with a fading rate of 80.

FIG. 13 shows the performance for MOK, for M=16 in Rician fading channelwith a fading rate of 80.

FIG. 14 shows the code set of complementary codes is much richer thanthe set of Walsh codes used in MOK.

FIG. 15 depicts a noncoherent CCK detector.

FIG. 16 compares the performance of coherent and noncoherent detectorsfor CCK in AWGN.

FIG. 17 shows the performance for CCK in Rician fading channel with afading rate of 10.

FIG. 18 shows the performance for CCK in Rayleigh fading channel with afading rate of 40.

FIG. 19 shows the performance for CCK in Rician fading channel with afading rate of 40.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows the block diagram of the system including both modulationand demodulation as well as the fading channel over which the MOK signalis transmitted. On the transmission (modulation) side the data is inputto a convolution encoder, which encodes the data. The encoded data isoutput from the convolutional encoder into an interleaver. The output ofthe interleaver is input into an M-ary orthogonal modulator, whichoutputs the signal to a channel. On the receiver (demodulation) side thesignal is detected and demodulated by an M-ary orthogonal demodulator.The output of the demodulator is input to a deinterleaver. The output ifthe deinterleaver is input to the MAP decoder, which decodes the data.Channel estimation is then performed by a channel estimator. The channelestimation metrics are then introduced into the M-ary orthogonalnon-coherent demodulator in a feedback model to re-demodulate the signalcoherently. The steps of interleaving and de-interleaving are optionalbut advantageous. The transmitted signal s(t) is given by

$\begin{matrix}{{s(t)} = {A{\sum\limits_{k = {- \infty}}^{\infty}{\alpha_{k}\left( {t - {kT}} \right)}}}} & (1)\end{matrix}$where α_(k)(t) is a symbol from an orthogonal set of symbols to betransmitted during the k^(th) symbol time interval.

${\alpha_{k}(t)} = {\sum\limits_{l = 1}^{M}{\alpha_{k}^{l}{p\left( {t - {lT}_{c}} \right)}}}$where α_(k) ^(l) is the l^(th) chip of the k^(th) symbol. p(t-lT_(c)) isthe chip waveform of arbitrary shape and unit energy.

The type of modulation considered here is called M-ary Orthogonal Keying(MOK). FIG. 2 shows the method to construct the signal set for MOK. Eachsymbol is composed of M chips, which will represent log₂ M coded databits. This set of symbols is called Hadamard-Walsh orthogonal sequences.It can be verified that any two vectors resulting from this mapping haveinner products that are exactly zero, and hence all M waveforms areorthogonal to one another.

Defining E_(b) as the energy per data bit. Now define E_(c)=E_(b)r_(c)as the energy per coded bit, where r_(c) is the convolutional code rate.Every b=log₂ M coded bits will be transmitted as one of the MOK symbols.Each MOK symbol consists of M chips, the energy per symbol isE_(s)=bE_(c), and the energy per chip is given by E_(ss)=E_(s)/M. Thatis, the energy per symbol is the bit energy times the convolutional coderate.

The optimum noncoherent detector for Hadamard-Walsh orthogonalmodulation is a bank of M orthogonal noncoherent correlators, as shownin FIG. 3, while the optimum coherent receiver is shown in FIG. 4.

FIG. 3 depicts the noncoherent detector/demodulator of the MOK receiver,which is used for a first pass through the feedback loop. Thereafter,the output of the noncoherent detector/demodulator is used as areference to the coherent detector/demodulator of the MOK receiver,which is depicted in FIG. 4. The apparatus used to detect/demodulate MOKsymbols, therefore, comprises both the noncoherent detector/demodulatordepicted in FIG. 3 and the coherent detector/demodulator depicted inFIG. 4.

Refering first to FIG. 3, the signal received from the fading channel ismultiplied by sin (ωt) and cos (ωt). Each of the products are then eachpassed through normalized matched filters resulting in real andimaginary components of the received signal. Each of these components issampled at a clock rate of 1/T_(C), where T_(C) represents the chipduration, which is the symbol duration divided by M. Since it is knownat this point that a symbol has been received but not which symbol, eachof the possible symbols is multiplied by the real and imaginarycomponents of the received signal, respectively, and summed. That is,

${z_{l}^{I}(k)} = {\sum\limits_{l = 1}^{M}{{r_{I}(l)}{s(l)}}}$${z_{l}^{Q}(k)} = {\sum\limits_{l = 1}^{M}{{r_{Q}(l)}{s(l)}}}$where r_(l)(l) and r_(Q)(l) are the l^(th) samples of the receivedsignal, s_(l)(l) is the l^(th) sample of M possible symbols and theresults z_(l) ^(I) and z_(l) ^(Q) are the in-phase and quadraturecomponents of the combination of the received signal, the multipathdistortion, any other interference and noise. That is, z_(l) ^(I) andz_(l) ^(Q) are in-phase and quadrature components of a modified versionof the desired signal. These in-phase and quadrature components are thensquared and added together on a component-by component basis resultingin [z_(l) ^(I)*(k)]²+[z_(l) ^(Q)(k)]². This further results in z_(l),which is fed into a MAP or Viterbi decoder and a metric calculator, theoutput of which is a tentative decision with respect to the symbolstring. This then becomes the reference signal c* used in FIG. 4 forfurther coherent demodulation or re-demodulation of the received signal.

The coherent detection/demodulation depicted in FIG. 4 follows roughlythe same logic as FIG. 3 but it is no longer necessary to generate animaginary component because a reference signal is now available. Thedecision resulting from the coherent detection/demodulation is improvedover the noncoherent detection/demodulation. Further iterations provideeven further improvements. The number of iterations will vary dependenton the environment and can be stopped when the recognition improvementor gain diminishes with the effort. That is, the gain ceases to increaseproportionately to the effort.

The received signal is given byr(t)=c(t)s(t)+n(t)  (2)where n(t) is AWGN with power spectral density N_(o) in the real andimaginary parts; and c(t) represents the flat frequency nonselectiveRician fading channel complex gain, with autocorrelation function:

$\begin{matrix}{{R_{c}(\tau)} = {\sigma_{8}^{2}\left( {\frac{K}{1 + K} + {\frac{1}{1 + K}{J_{o}\left( {2\pi\; f_{D}\tau} \right)}}} \right)}} & (3)\end{matrix}$where K is the ratio between the line of sight power and the scatteredpower, J₀ is the zero order modified Bessel function of the first type;f_(D) is the fading bandwidth; τ is the timing difference.Define

$J_{\max} = \frac{R_{s}}{2R_{f}}$where R_(s) is the chip rate and R_(f) is the fading rate.

The normalizing matched filter, with impulse response p*(−t)/(√{squareroot over (N₀)}), has an output given byr(k _(i))=u(k _(i))α_(k) ^(i) +n(k _(i))where k_(i) represent the time instant of the i^(th) chip of the k^(th)symbol. The Gaussian noise samples n(k) are white with unit variance,and the complex symbol gain u(k) has mean

${E\left\lbrack {u(k)} \right\rbrack} = {\sqrt{\gamma_{ss}}\sqrt{\frac{K}{K + 1}}}$and variance

$\sigma_{u}^{2} = {\gamma_{ss}\frac{1}{K + 1}}$where the average SNR is given by

$\gamma_{ss} = \frac{E_{ss}}{N_{o}}$

A simplified decision metric was derived for Rayleigh fading channelswith noncoherent detection. The metric for the more generalized Ricianfading channel is now derived. For M-ary orthogonal signals, the outputof the filters is denoted by z_(i), i=1, . . . , M. As shown in FIG. 1,the proposed system has a convolutional encoder/decoder pair that needssoft information from the MOK detector/demodulator. Therefore, it isnecessary to derive the log likelihood ratio (LLR) for the data and codebits. The LLR is defined by

$L = {\ln\left( \frac{p_{1}\left( Z^{\prime} \right)}{p_{o}\left( Z^{\prime} \right)} \right)}$where Z′=(z₁, z₂, . . . , z_(M)) is the vector whose components are theM correlator (coherent or noncoherent) outputs. Consider the first bit(not chip) of the symbol and calculate its LLR. For Hadamard-Walshcodes, the first M/2 sequences will have a “0” in the first position,while the last M/2 sequences will have a “1” in the first position.Hence, given equiprobable input sequences, the LLR for the first bit isgiven by

${p_{1}(z)} = {{2/M}{\sum\limits_{m = 1}^{M/2}{p\left( {Z^{\prime}/s_{m}} \right)}}}$${p_{o}(z)} = {{2/M}{\sum\limits_{m = {{M/2} + 1}}^{M}{p\left( {Z^{\prime}/s_{m}} \right)}}}$where s_(m) is the m^(th) sequence, and p(Z/s_(m)) is the probabilitydensity function (pdf) of the M correlator outputs given that sequence mwas sent. Because of the orthogonality of the sequences we can writethese joint pdfs of the correlator outputs asp(Z′/s _(m))=p _(c)(z _(m))Π_(m′≠m) p _(N)(z _(m′))where p_(c)(z) is the pdf of the correlator output corresponding to thecorrect signal sent, while p_(N)(z) pertains to all the M−1 others. Inthe following subsections we will deal with the coherent and noncoherentreceivers for the more general Rician fading channels.

The input to the detector is Rician distributed withf(r)=2(K+1)re ^(−(K+1)r) ² ^(−K) I ₀[2r√{square root over(K(K+1))}]  (4)where I₀ is the zeroth order modified Bessel function of the first kind.

For the noncoherent detector shown in FIG. 3, the received signal isgiven byr(k _(i))=u(k _(i))α_(k) ^(i) +n(k _(i))Now the receiver forms the signals representing the real and imaginaryparts of rr _(I) =Re(r)r _(Q) =Im(r)where Re(.) represents the real part and Im(.) represents the imaginarypart.

${z_{l}^{I}(k)} = {\sum\limits_{l = 1}^{M}{{r_{I}(l)}{s(l)}}}$${z_{l}^{Q}(k)} = {\sum\limits_{l = 1}^{M}{{r_{Q}(l)}{s(l)}}}$z_(l)(k) = [z_(l)^(I)(k)]² + [z_(l)^(Q)(k)]²For the output of the M−1 noncoherent detectors corresponding to thenoise only, z_(i) ^(Q)(k) and z_(i) ^(I)(k) are Guassian with zero mean,and z_(i)(k) is of exponential distribution. The pdf of z_(i)(k) isgiven byp _(N)(z)=e ^(−z)

The output of the detector corresponding to the transmitted signal isgiven by

${p_{c}(z)} = {\frac{1}{1 + {\frac{1}{k + 1}\frac{E_{s}}{N_{o}}}}{\mathbb{e}}^{{- \frac{z}{({1 + {\frac{1}{K + 1}\frac{E_{s}}{N_{o}}}})}} - {\frac{K}{K + 1}\frac{E_{s}}{N_{o}}}}{I_{o}\left\lbrack {2\sqrt{\frac{z}{1 + {\frac{1}{K + 1}\frac{E_{s}}{N_{o}}}} - {\frac{K}{K + 1}\frac{E_{s}}{N_{o}}}}} \right\rbrack}}$Now the LLR for the first bit is given by

$L = {\ln\left\lbrack \frac{\sum\limits_{m = 1}^{M/2}{{p_{c}\left( z_{m} \right)}{\prod\limits_{m^{\prime} \neq m}{p_{N}\left( z_{m^{\prime}} \right)}}}}{\sum\limits_{m = {{M/2} + 1}}^{M}{{p_{c}\left( z_{m} \right)}{\prod\limits_{m^{\prime} \neq m}{p_{N}\left( z_{m^{\prime}} \right)}}}} \right\rbrack}$$L = {\ln\left\lbrack \frac{\sum\limits_{m = 1}^{M/2}{{p_{c}\left( z_{m} \right)}/{p_{N}\left( z_{m} \right)}}}{\sum\limits_{m = {{M/2} + 1}}^{M}{{p_{c}\left( z_{m} \right)}/{p_{N}\left( z_{m} \right)}}} \right\rbrack}$$L = {\ln\left\lbrack \frac{\sum\limits_{m = 1}^{M/2}{{\mathbb{e}}^{\frac{z_{m}{E_{s}/N_{o}}}{K + 1 + {E_{s}/N_{o}}} - {\frac{K}{K + 1}{E_{s}/N_{o}}}}{I_{o}\left( {2\sqrt{\frac{z_{m}}{1 + {\frac{1}{K + 1}\frac{E_{s}}{N_{o}}}}\frac{K}{K + 1}\frac{E_{s}}{N_{o}}}} \right)}}}{\sum\limits_{m = {{M/2} + 1}}^{M}{{\mathbb{e}}^{\frac{z_{m}{E_{s}/N_{o}}}{K + 1 + {E_{s}/N_{o}}} - {\frac{K}{K + 1}{E_{s}/N_{o}}}}{I_{o}\left( {2\sqrt{\frac{z_{m}}{1 + {\frac{1}{K + 1}\frac{E_{s}}{K_{o}}\frac{K}{K + 1}\frac{E_{s}}{N_{o}}}}}} \right)}}} \right\rbrack}$In the case of Rayleigh fading, K=0 and the LLR reduces to

$L = {\ln\left\lbrack \frac{\sum\limits_{m = 1}^{M/2}{\mathbb{e}}^{\frac{z_{m}{E_{s}/N_{o}}}{1 + {E_{s}/N_{o}}}}}{\sum\limits_{m = {{M/2} + 1}}^{M}{\mathbb{e}}^{\frac{z_{m}{E_{s}/N_{o}}}{1 + {E_{s}/N_{o}}}}} \right\rbrack}$While in the case of Gaussian noise channel (no fading), K=∞

$L = {\ln\left\lbrack \frac{\sum\limits_{m = 1}^{M/2}{I_{o}\left( {2\sqrt{z_{m}\frac{E_{s}}{N_{o}}}} \right)}}{\sum\limits_{m = {{M/2} + 1}}^{M}{I_{o}\left( {2\sqrt{z_{m}\frac{E_{s}}{N_{o}}}} \right)}} \right\rbrack}$The resulting LLR is the summation of either exponentials, modifiedBessel functions or the product of both. A very good approximation forthese types of functions is to choose the maximum term in the summation.The approximate LLR is given by

$L = {{\max_{m = 1}^{M/2}z_{m}} - {\max_{m = {{M/2} + 1}}^{M}z_{m}}}$The performance of the optimum metric is very close to that of thesimplified metric, the approximate LLR is used for decoding of theconvolutional code. There is almost no gain or advantage in using theexact metric while the computational advantage gained by using thesimplified metric is huge.

The coherent detector is shown in FIG. 4. In this case the LLr is givenby

$L = {{{\ln\left\lbrack \frac{\sum\limits_{m = 1}^{M/2}{\mathbb{e}}^{z_{m}{E_{s}/N_{o}}}}{\sum\limits_{m = {{M/2} + 1}}^{M}{\mathbb{e}}^{z_{m}{E_{s}/N_{o}}}} \right\rbrack}\mspace{14mu}{where}\mspace{14mu} z_{m}} = {\sum\limits_{l = 1}^{M}{{{Re}\left( {y_{l}c_{l}^{*}} \right)}{s_{m}(l)}}}}$where c_(i)* is the channel estimate. A very good approximation for thisexpression is

$L = {{\max_{m = 1}^{M/2}z_{m}} - {\max_{m = {{M/2} + 1}}^{M}z_{m}}}$

In almost all the practical systems that implement some form of MOK,noncoherent detection is used. For AWGN, the difference between thecoherent and noncoherent detection of MOK is very small. FIG. 5 showsthe performance of coherent and noncoherent detection of orthogonallymodulated convolutionally coded signals in AWGN environment. It can benoticed that the difference between the two schemes is less than 1 dBfor BER≦10⁻³.

However, the difference in performance between coherent and noncoherentdetection of MOK increases significantly with the increased rate offading (J_(max)). This is due to the fact that the chips forming thesymbol may be subject to different amplitude and phase distortion in thefading channel. In coherent detection, the fading channel is assumedfully known such that the effect of the changing amplitude and phasewill not deteriorate the performance. Two alternate methods that use theconcept of iterative decoding are presented to enhance the performanceof MOK based systems without additional signal components (i.e.,additional pilot signal).

The concept of iterative decoding was spurred on by the introduction ofTurbo codes. The performance of Turbo codes approached the Shannon limitfor the channel capacity, which provoked a great deal of interest in theresearch community. Generalizing the use of iterative decoding has beenproposed to be used in the different blocks of the receiver. All thereceiver modules use soft input soft output (SISO) operations in orderto maximize information exchange between them. A method that uses theconcept of iterative decoding for iterative detection of MOK signals isnow presented.

FIG. 1 shows the block diagram of the noncoherent-coherent system. Thefirst method is, as indicated by its name, an iterative algorithm where,a form of coherent detection follows the first standard noncoherentdetector. Following the noncoherent detector and MAP decoder, the softoutputs of the decoder are used to calculate the probabilities of thesymbols such that it can be used to estimate the channel. The presenceof the interleaver here has a double advantage. The standard use of theinterleaver is the prevention of the error bursts that can happen indeep fade periods. The other advantage of the interleaver is making theoutputs of the decoder and channel estimator independent. Theinterleaver makes the bits affecting the decisions on a certain bit dueto the decoding algorithm differ from the bits used to estimate thefading channel at the time of that bit.

Denote the reliability information of the data and code bits at theoutput of the decoder with soft outputs (i.e., MAP,SOVA(soft outputViterbi algorithm), . . . ) by L(m). To calculate the probabilities ofthe data and code symbols use,

${p\left( {{x(m)} = 1} \right)} = \frac{{\mathbb{e}}^{L{(m)}}}{\left( {1 + {\mathbb{e}}^{L{(m)}}} \right)}$The above probabilities could not be used directly to estimate thechannel. The bit probabilities are used to calculate the probabilitiesof the chips, which were physically transmitted through the channel.

First calculate the probability of symbols using

$\begin{matrix}{{{p_{s}(k)} = {\prod\limits_{l = 1}^{\log_{2}M}\left( {{\left\lbrack {1 - U_{l}} \right\rbrack\left\lbrack {1 - {p(l)}} \right\rbrack} + {U_{l}{p(l)}}} \right)}},{k = 1},2,\ldots\mspace{11mu},M} & (5)\end{matrix}$where U_(j)=1 if the j^(th) bit=1 for this symbol, if the j^(th) bit=0,U_(j)=0, p(l) is the probability that bit l of the symbol=1. Thiscalculation is repeated for every symbol instant, i.e., M differentprobabilities are calculated for every symbol instant.

Following the calculation of the symbols probabilities, theprobabilities of the chips are calculated. The probability of the l^(th)chip is given by

$\begin{matrix}{{p_{ss}(l)} = {\sum\limits_{k = 1}^{M}{h_{k}{p_{s}(k)}}}} & (6)\end{matrix}$where p_(ss)(l) is the probability that chip l equals 1, h_(k)=1 if chipl=1 in symbol k and h_(k)=0 if chip l=−1 in symbol k.

Now that the probability of the chips has been calculated, it isnecessary to estimate the channel using this information. A Wienerfilter is used in the filtering of the chips to obtain the channelestimate. The filter is designed as explained below. Only one filter isnecessary for all points. The channel estimate is given by

${\hat{c}(m)} = {\sum\limits_{j = {- D}}^{D}{{{h(j)}\left\lbrack {{2{p_{ss}\left( {m + j} \right)}} - 1} \right\rbrack}{r\left( {m + j} \right)}}}$where 2D+1 is the order of the filter, assumed odd. Following thechannel estimator, coherent detection is performed. A number ofiterations of the steps of demodulating said M-ary orthogonallymodulated signal, calculating a metric, decoding said signal,calculating probabilities of different symbols for each symbol instance,and estimating a fading channel responsive to calculating theprobabilities could be repeated until no gain or recognition improvementis detected. In the alternative, a threshold value of recognitionimprovement could be preset and the iterations could be stopped oncethat threshold is attained. That is, the threshold value could be based,for example, on no change in a specific decimal place or a comparisonbetween the recognition improvement in two iterations versus acalculation of the effort per iteration. From the simulation results, inmost instances two iterations after the initial noncoherent detector wasenough to capture almost all of the gain from this scheme.

An alternate method could be used to perform quasi-coherent detection.It can be noticed that all the different MOK symbols start with a “1”which makes these signals, by design, good for SAD demodulationtechniques. The rate of change of the fading dictates the rate ofinsertion of the known symbols. In the case of MOK signals, the knownsymbols are present with rate J=M. If J<J_(max) then there is no need tocomplicate the signal by inserting more known symbols, and the SADmethods could be used without adding more known symbols. The channelestimate at the first step is obtained using only the known first chip.Following the first decoding step, the unknown chips are also used toestimate the channel exactly as in the noncoherent-coherent scheme.

The forward error control code used is rate ½, 4 state convolutionalcode with generator polynomials 5 ₈ and 7 ₈. Following the firstdecoding step, 2 more decoding steps that use the known symbols wereconducted. The BER after the last step is shown in the figures andreferred to as “Iter. Noncoh.” And “Iter. SAD”, except in FIG. 6 where 2iterations were shown for the “Iter. Noncoh.” algorithm.

FIG. 6 to FIG. 9 show the performance of MOK, for M=8 in Rayleigh andRician fading channels for different fading rates, while FIG. 10 to FIG.13 show the same for M=16. A number of trends could be observed. ForM=8, the SAD scheme is better than the noncoherent scheme, and theperformance of the iterative algorithms is very good. In almost all thecases, the iterative algorithm cut the difference between the coherentand either SAD or noncoherent by almost three quarters. In very fastRaleigh fading case (J_(max)=10 and K=0), we notice that there is anerror floor for the noncoherent case while the SAD algorithm does notsuffer from that (at least in the shown range). Also the iterativealgorithm for noncoherent detection overcame the error floor after 2iterations. For the most favorable channel (J_(max)=40 K=10), we findthat the iterative algorithms' performance is extremely close (≈0.2 dB)to the coherent detection case.

For M=16, similar trends appear to hold, the only notable difference isthat the performance of the noncoherent detector is sometimes betterthan the performance of the SAD scheme, most notably at low E_(b)/N₀ invery fast Raleigh fading (J_(max)=20 and K=0). A possible explanation ofthis, is that at low E_(b)/N₀ in fast fading, the noise effect maybe asdominant as fading, and the channel estimate produced by the SAD schemeat low E_(b)/N₀ is less reliable than the noncoherent case and lessreliable than the estimate in the case of M=8 as the time intervalbetween successive known chips is larger relative to the time betweenthe chips (used by noncoherent detector). At high E_(b)/N₀, fadingdictates the performance and the SAD scheme performance is better thanthe noncoherent scheme.

Recently, Harris Semiconductors and Lucent Technologies developed anapproach called complementary code keying (CCK) to be used for high rateindoor wireless local area networks (WLAN). The IEEE 802.11 subcommitteeadopted CCK as the basis for the physical layer of high speedtransmission. CCK is a form of MOK modulation which uses aninphase-quadrature modulation architecture with complex signalstructure. CCK is a modulation where one of M unique (orthogonal ornearly orthogonal depending on the number of codes needed) signalcodewords is chosen for transmission.

For M-ary biorthogonal keying (MBOK) there are 8 chips that have amaximum vector space of 256 codes, which there are sets of 8 that areorthogonal. Two independent vectors are selected for the orthogonal Iand Q channels which modulate three bits on each. On additional bit canbe used to DPSK each of the resulting I and Q codes. The code set ofcomplementary codes is much richer than the set of Walsh codes used inMOK, as shown in FIG. 14. For CCK there are 4⁸=65536 possible codewords,and sets of 64 that are nearly orthogonal. The CCK codewords depicted inFIG. 14 lie in two planes, the page being a first plane and a secondplane perpendicular to the first plane. This second plane is indicatedby slanted lines. The codewords are the components of a signalconstellation.

The IEEE 802.11 standard adopted CCK for the transmission of either 5.5Mbps using a CCK code of length 8 to carry 4 bits or 11 Mbps using a CCKcode of length 8 carrying 8 bits. For the half data rate version, asubset of 4 of the 64 vectors that have superior coding distance isused. The first 4 rows of table 1 shows a possible set. The code setused is given byC=[e ^(ø1+ø2+ø3+ø4) ,e ^(ø1+ø3+ø4) ,e ^(ø1+ø2+ø4) ,−e ^(ø1+ø4) ,e^(ø1+ø2+ø3) ,e ^(ø1+ø3) , −e ^(ø1+ø2) ,e ^(ø1)]Where

-   -   ø_(j): 0,π/2, π, 3π/2, j=1, 2, 3, 4        for the 256 code set and    -   ø₁: 0π/2, π, 3π/2    -   ø₂: π/2, 3π/2    -   ø₃: 0    -   ø₄: 0,π        for the 16 code set which is shown in table 1.

Since CCK symbols are QPSK in nature, they simultaneously occupy boththe I and Q channels. The multipath performance of CCK is better thanMOK and MBOK (M-ary biorthogonal keying) due to the lack of cross-railinterference. One of the advantages of CCK over MBOK is that it suffersless from multipath distortion in the form of cross coupling of the Iand Q channel information. The information in CCK is encoded directlyonto complex chips, which cannot be cross-couple corrupted by multipathdistortion or fading. This superior encoding technique avoids thecorruption resulting from half the information on the I channel and halfon the Q channel as in MBOK, which is easily cross couple corrupted withthe multipath phase rotation.

As mentioned before, one of the main advantages of MOK is the ability todemodulate the signal noncoherently. It is not possible to demodulate“simply” modulated MBOK or CCK signals noncoherently. By “simply” wemean assigning the code directly depending on the log₂ M bits, where Mis the total number of codewords.

However, in the scheme adopted by the standard, signals can bedemodulated noncoherently. For example, for the 5.5 Mbps CCK mode, theincoming data is grouped into 4 bit nibbles where two of the bits selectthe spreading function out of a set of 4 codes while the remaining twobits then differential QPSK (DQPSK) the carrier. Applying this to thecode set shown in table 1, one of the first four codes is selected by 2of the four data bits, the other 2 bits will rotate the selected code by0, π/2, π, 3π/2.

TABLE 1 CCK codewords Codeword 1 2 3 4 5 6 7 8 1 1 j 1 −j −1 −j 1 −j 2 1j 1 −j 1 j −1 j 3 1 −j 1 j 1 −j −1 −j 4 1 −j 1 j −1 j 1 j 5 j −1 j 1 −j1 j 1 6 j −1 j 1 j −1 −j −1 7 j 1 j −1 j 1 −j 1 8 j 1 j −1 −j −1 j −1 9−1 −j −1 j 1 j −1 j 10 −1 −j −1 j −1 −j 1 −j 11 −1 j −1 −j −1 j 1 j 12−1 j −1 −j 1 −j −1 −j 13 −j 1 −j −1 j −1 −j −1 14 −j 1 −j −1 −j 1 j 1 15−j −1 −j 1 −j −1 j −1 16 −j −1 −j 1 j 1 −j 1

For example, if the first two bits chose the first code, the next twobits are encoded differently as follows. Denote the two bits that changethe phase as d₁ and d₂. The phase at the j^(th) time instant is given by

$\begin{matrix}{\Phi_{j} = {\Phi_{j - 1}{\mathbb{e}}^{\frac{{\mathbb{i}}{({{2d_{2}} + d_{1}})}}{2\pi}}}} & (7)\end{matrix}$Therefore, if the first 2 bits chose the first code, depending on thesecond two bits and the previous phase, code number 1, 5, 9, or 13 is tobe transmitted.

The advantage of this scheme is the reduced complexity that can be usedto demodulate it. First the detector/demodulator decides which one ofthe four basic codes is transmitted which can be done noncoherently asshown in FIG. 15. The apparatus depicted in FIG. 15 is similar to thatdepicted in FIG. 3 but only four basic codes are transmitted andreceived. The symbols s_(i)*(k) are the complex conjugates of thepossible codes. The MAP decoder or Viterbi decoder and metric calculatorhave been replaced with an algorithm that uses the argument of themaximum z_(j) to decide on the first two bits and the maximum of z_(j)to decide on the remaining two bits in a feedback loop with a one bitdelay.

z^(I) _(j)(k) and z^(Q) _(j)(k) are calculated as follows

${z_{j}^{I}(k)} = {\sum\limits_{l = 1}^{M}{{Z_{I}(l)}{s_{j}^{\circ}(l)}}}$${z_{j}^{Q}(k)} = {\sum\limits_{l = 1}^{M}{{Z_{Q}(l)}{s_{j}^{\circ}(l)}}}$z_(j)(k) = [z_(j)^(I)(k)]² + [z_(j)^(Q)(k)]²where j=1,2,3,4, s_(j) is the j^(th) codeword. * represents complexconjugate. Following this step, the argument of the maximum z_(j) andthe value of the maximum z_(j) are used to decide on the first two bitsand differentially demodulate the remaining two bits.

Define u as the argument of the maximum z_(j) and v as the value of themaximum z_(j). u is used to decide on the first two bits, while v isindependently differentially demodulated to decide on the other 2 bits.

As will be shown in the results, for fading channels, the performance ofthe noncoherent detector of CCK is significantly worse than that ofcoherent detector where the data and code bits directly choose acodeword from the CCK codeword set, and a perfect channel estimate isavailable.

For AWGN channels, the performance of the noncoherent detector is worsethan that of the coherent detector for up to 2 dBs unlike the simple MOKcase where the difference may be as low as 0.5 dB. FIG. 16 shows theperformance of convolutionally encoded CCK symbols with coherent andnoncoherent detectors for the codewords shown in table 1.

Note that the modulation process differs for both cases. The input tothe noncoherent detector is as explained in the previous section, whilea direct mapping is used in the coherent detector case where 4 bitsdirectly choose one of the 16 codewords.

The increased difference in performance between both detectors is due todifferential encoding needed for the noncoherent detector. As CCK is ageneralized form of MBOK, there is no way to apply noncoherent detectiontechniques for simply encoded signals. The complex method of encodingdescribed earlier, is the key factor enabling noncoherent detection.

As will be shown below in the numerical results, the performance ofnoncoherent detectors of CCK in fading channels is much worse than thatof coherent detectors. A modification to the current CCK method improvesthe performance significantly over the noncoherent CCK system proposedby Lucent technologies and Harris semiconductors. As mentionedpreviously in the MOK case, the knowledge of the first chip of all thesymbols, makes SAD demodulation a viable alternative for MOK signals infading channels. In the present method an extra chip is added at thebeginning of each symbol, say “1”, that can be used to estimate thefading channel. This chip will increase the symbol size from 8 to 9chips, which is a minimal increase relative to the performanceimprovement gained.

The method used for channel estimation is similar to the SAD-coherenttechnique used for MOK. At the beginning, the added known chips are usedto estimate the channel at the different chip positions within thesymbol using optimized Wiener filters as described below. Coherentdetection is performed using the channel estimate obtained by the knownchips, and a first decoding step is performed.

Equation 5 shows the calculation of the probabilities of the differentsymbols knowing the LLR at the output of the decoder. Following, theexpected value of the conjugate of every chip given the symbolprobabilities is calculated as follows

${E_{pss}(l)} = {\sum\limits_{k = 1}^{M}{h_{k}{p_{s}(k)}}}$

-   -   h_(k)=1 if chip l=1 in symbol k    -   h_(k)=i if chip l=−i in symbol k    -   h_(k)=−1 if chip l=−1 in symbol k    -   h_(k)=−i if chip l=i in symbol k        and the channel estimate is calculated by taking into        consideration the known and unknown chips

${\hat{c}(m)} = {\sum\limits_{j = {- D}}^{D}{{h(j)}{E_{pss}\left( {m + j} \right)}{r\left( {m + j} \right)}}}$where h(j) is an optimum Wiener filter designed assuming perfectknowledge of the chips, 2D+1 is the filter length. This channel estimateis used to coherently demodulate the incoming signal and a new decodingstep is performed.

FIG. 17 to FIG. 19 shows the performance of different CCK schemes infading channels. The error control coding used is a rate ½, 4 stateconvolutional code with generator polynomials 5 ₈ and 7 ₈. Following thefirst decoding step, 2 more decoding steps that use the unknown symbolswere conducted. The BER after the first step is denoted “SAD”. “Diff.”refers to the standard differential-noncoherent detector. It is veryclear that for fading channels, the performance of the SAD scheme issignificantly better than that of differentially detected CCK. Thereason is that in the fading channels, differential detection'sperformance is affected greatly. Note that differential modulation isperformed on the symbol level (not chips) which makes the time intervalbetween successively demodulated bits relatively large for low datarates. The SAD method overcomes this drawback and does not usedifferential detection. Iterative SAD gains approximately 0.5 dB overSAD.

The Wiener filter is based on the least-squares principle, i.e., itfinds the filter, which minimizes the error between the actual outputand the desired output of the filter.

The estimate of the fading channel is given by

$\begin{matrix}{{v(k)} = {{{{\underset{\_}{h}}^{\dagger}(k)}\underset{\_}{r}} = {\sum\limits_{i = {- D}}^{D}{{h^{\circ}\left( {i,k} \right)}{r({iJ})}}}}} & (8)\end{matrix}$

where ^(†) denotes conjugate transpose, and * denotes conjugate. r isthe vector formed from the samples of the output of the matched filterat the known symbol instants, i is the index of the known (SAD) symbolswhere −D≦i≧D and k is the position of the unknown data symbol in theframe where 1≦k≧J−1. Note that there are J−1 different filters used. TheWiener filter equation is given by{tilde over (R)}h (k)= w (k)  (9)where {tilde over (R)} is the autocorrelation matrix of size 2D+1defined by

$\overset{\sim}{R} = {\frac{1}{2}{E\left\lbrack {\underset{\_}{rr}}^{\prime} \right\rbrack}}$and the J−1 length 2D+1 vectors w(k) are given by

${\underset{\_}{w}(k)} = {\frac{1}{2}{E\left\lbrack {{u^{*}(k)}\underset{\_}{r}} \right\rbrack}}$

The channel under consideration is Rician as described in equation (3),and hence {tilde over (R)} and w(k) are given by

$\begin{matrix}{R_{ij} = {{\frac{\gamma}{K + 1}{\frac{\left( {J - 1} \right)}{J}\left\lbrack {K + {J_{o}\left( {\pi\frac{\left( {i - j} \right)J}{J_{\max}}} \right)}} \right\rbrack}} + {\left\lbrack {{\gamma\frac{\left( {J - 1} \right)}{J}\frac{\left. {2\left( {{K_{u}L} - 1} \right)} \right)}{3N}} + 1} \right\rbrack\delta_{i,j}}}} \\{{w_{i}(k)} = {\frac{\gamma}{K + 1}{\frac{\left( {J - 1} \right)}{J}\left\lbrack {K + {J_{o}\left( {\pi\frac{\left( {{iJ} - k} \right)}{J_{\max}}} \right)}} \right\rbrack}}}\end{matrix}$where i, j=−D, . . . , −1,0,1, . . . ,D and δ_(i,j) is the Kroneckerdelta.

A novel method and system to improve the performance of MOK signals infading channels has been described. The two methods presented improvegreatly on the performance of simple noncoherent detectors of MOK, withminimal added complexity. From the numerical results it was clear thatthese methods approach the performance of coherent detectors within 0.2dB in Rician fading. For fast Rayleigh fading, the error floor presentusing the noncoherent detector was removed using the iterative algorithmpresented.

For CCK, the new method presented enhances greatly the performance andpotential of using CCK for fast fading terrestrial mobilecommunications. The noncoherent system proposed in the prior art to beused for very high rate WLAN could not be used for fast fading channelsas its performance degrades greatly. The scheme presented here addsminimal complexity and has performance close to the coherent detectioncase.

The method and apparatus described herein may be extended to signalsreceived and detected over multipath channels. That is, the method andapparatus will work on multipath channels and are not limited to singlemode channels with flat fading. This could be implemented in severalways and is fairly complex implementationally. Most, if not all,components in the receiver situated before the decoder will increasewith the number of paths.

It should be clear from the foregoing that the objectives of theinvention have been met. Although particular embodiments of the presentinvention have been described and illustrated, it should be noted thatthe invention is not limited thereto since modifications may be made bypersons skilled in the art. The present application contemplates any andall modifications that fall within the spirit and scope of theunderlying invention disclosed and claimed herein.

1. A method for use in a receiver for detecting and demodulating aninput signal coded in accord with M-ary orthogonal keying (MOK)comprising the steps of: a. receiving said coded signal over a channel;b. demodulating M-ary orthogonally modulated symbols from said codedsignal to form demodulated signals; c. calculating a metric for thedemodulated signals; d. decoding said symbols with aid of the metric; e.calculating probabilities of different symbols for each symbol instance;f. estimating a fading channel with aid of the calculated probabilities;and g. demodulating coherently M-ary orthogonally modulated symbols fromsaid coded signal to form demodulated signals using said channelestimate that is calculated with aid of, said probabilities to form newmodulated signals, and passing control to step c.
 2. The method of claim1 where said passing of control to step c is executed at most twicebefore deciding on the symbols that are contained in said coded signal.3. The method of claim 1 where said demodulating in step b is quasicoherent.
 4. The method of claim 1 where said signal is coded with aconvolutional outer code.
 5. The method of claim 1 where said signal iscoded with a non-convolutional outer code.
 6. The method according toclaim 1, where said demodulating in step b is non-coherent.
 7. Themethod of claim 1 where step g is stopped when improvement in saidmetric is below a preselected level.
 8. The method of claim 1 where stepg is stopped when recognition improvement in step d is outweighed byeffort to achieve the recognition improvement.
 9. The method of claim 1where the input signal coded in accord with M-ary orthogonal keying iscomplementary code keying (CCK) transmitting at 5.5 Mbps rate using aCCK code of length 8 carrying 4 bits, or transmitting at 11 Mbps using aCCK code of length 8 carrying 8 bits, and the demodulating of step b isnon-coherent.